cylindrical shells, elastoplastic loss of stability, elastic filler, Winkler foundation.

Comparison of the results of calculations of contact interaction and loss of stability of elastoplastic cylindrical shells with an elastic thick-walled filler, performed on the basis of two approaches: from the standpoint of continuum mechanics and the theory of Timoshenko–type shells with a Winkler base is presented. Both approaches allow solving the problems of deformation and stability of non–sloping shells, taking into account geometric nonlinearities. The statement from the perspective of continuum mechanics makes it possible to approximate the shell in thickness by a number of layers of finite elements. The constitutive relations are formulated in Lagrange variables using a fixed Cartesian or cylindrical coordinate system as a reference. Kinematic relations are recorded in the metric of the current state. The elastic-plastic properties of shells are described by the theory of plastic flow with isotropic hardening. The equations of motion follow from the balance of the virtual powers of the jobs. In the first approach, the contact interaction of a shell and an elastic body is modeled by the conditions of nonpenetration along the normal and free slip along the tangent. In the second approach, the contact interaction of the elastic filler with the shell is modeled by the Winkler base. Both approaches allow one to describe the nonlinear subcritical deformation of shells of revolution with an elastic filler, to determine the limiting (critical) loads in a wide range of loading rates, taking into account the geometric imperfections of the shape. The area of applicability of the Winkler hypothesis is estimated for the contact interaction of a shell with an elastic medium, depending on the stiffness and thickness of the base.

Bazhenov, Valentin Georgievich, Dr. Sci. Phys. & Math., Professor,Chief Researcher, Doctor of Physical and Mathematical Sciences, Professor, Research Institute of Mechanics, National Research Lobachevsky State University of Nizhni Novgorod, Russia,

Nagornykh, Elena Vladimirovna, Nagornykh, Elena Vladimirovna, PhD of Physical and Mathematical Sciences, Assoc. Prof., National Research Lobachevsky State University of Nizhni Novgorod, Russia,

Samsonova, Daria Anatolievna Postgraduate student, Institute of Information Technology, Mathematics and Mechanics, National Research Lobachevsky State University of Nizhni Novgorod, Russia.